Question 76107
The demand and supply equations for a certain item are given by
D = 5p + 40
S= -p^2 + 30p -8
Find the equilibrium Price.
:
Equilibrium occurs when Demand = Supply, (D=S)
:
5p + 40 = -p^2 + 30p - 8
:
Form a quadratic equation on the left
+p^2 + 5p - 30p + 40 + 8 = 0
:
p^2 - 25p + 48 = 0
:
Use the quadratic equation to find p: a=1; b=-25; c=48:
{{{p = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{p = (-(-25) +- sqrt( -25^2 - 4 * 1 * 48 ))/(2*1) }}}
:
{{{p = (+25 +- sqrt( 625 - 192 ))/(2) }}}
:
{{{p = (+25 +- sqrt( 433 ))/(2) }}}
:
{{{p = (+25 + 20.8)/(2) }}}
:
{{{p = (+45.8)/(2) }}}
p = 22.9
and
{{{p = (+25 - 20.8)/(2) }}}
:
{{{p = (+4.2)/(2) }}}
p = 2.1
:
Check solution using p = 2.1, are both equations equal?
5p + 40 = 
5(2.1) + 40 = 50.5
and
-p^2 + 30p = 8 +
-(2.1^2) +30(2.1) -8 = 
- 4.41 + 63 - 8 = 50.6; a slight difference because our solution is not exact